The trouble with getting your licence converted by the time you start, is will you really have it before you start your training?
Getting your license converted depends on how quick your current CAA is at sending over your medical and license documents, then it depends on how long the wait is to get that paper work processed and a licensed issued by your new CAA.
I had a colleague who was offered a job, started the conversion process the next day, 3 months later no license, issues with his paperwork. Luckily the airline was understanding, and kept him on the ground 5 weeks later the licence came through.
4 months and 1 week it took them to get their new licence issued, they missed their company induction and type rating course, not good for the training department.
Secondly it could be used as a criteria to narrow down the applicants.
Good luck to all involved.